# Universality of cutoff for graphs with an added random matching

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Abstract:

We establish universality of cutoff for simple random walk on a class of random graphs defined as follows. Given a finite graph \$G=(V,E)\$ with \$|V|\$ even we define a random graph \$ G^*=(V,E \cup E')\$ obtained by picking \$E'\$ to be the (unordered) pairs of a random perfect matching of \$V\$. We show that for a sequence of such graphs \$G_n\$...More

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